We can conclude that there is a Borel set [1]}, namely \(\mathbb {Q}\) , that is not constructible from the usual topology. We might think that there is a direct relationship between sets of first category (see [2]}) and constructible sets, but this is false as \(\mathbb {Q}\)  is of first category and its complement, the irrational numbers, is of second category and both can not be constructed from  \(\mathcal {U}\) . Lemma REF  characterizes which sets are constructible.
